Review of N. Gisin, Collapse. What Else? in Collapse of the Wave Function, Edited by Shan Gao, Cambridge University Press 2018

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Summary:

Gisin begins by presenting his view of the quantum measurement problem. His viewpoint is generally that quantum mechanics is not consistent if the observer is treated as a quantum system. He first considers a dualist approach in which, “the world is made out of two sorts of stuff, one to which the quantum mechanical superposition principle applies and one to which it doesn’t apply.” In Sec. 12.2 the argument is given that the experimenter or theoretician does not need to be considered in order to investigate measurement. In Sec. 12.3 and 12.4 many-worlds and Bohm’s theory are reviewed, but neither is felt to resolve the problem. In Sec 12.5, the determinism in Newton’s theory is examined and why the non-locality or action-at-a-distance in gravitational theory bothered Newton. Gisin contends that determinism plus entanglement is intractable, and that effective collapses are needed in a theory.

In Sec. 12.6, dualism is revisited in more detail. Gisin does not believe that there can be a dualist solution and provides an argument as follows. Gisin denotes as the initial state of some quantum stuff that interacts with some non-quantum stuff . Then unitarily after an arbitrary short time the quantum and non-quantum stuff become entangled in the following manner:

   

Now Gisin states that if the non-quantum stuff can’t at all be in superposition, then the superposition state in the above equation can’t exist, “not even for a split of a second.” Gisin concludes then, “there would be instantaneous collapse also for the quantum stuff.”  

Gisin then advocates that superpositions such as the above can exist for a given small time, but then are washed away.  In Sec. 12.7, it is argued that deterministic generalizations of quantum mechanics are most often non-linear in density operator and that a non-deterministic generalization of Schrödinger’s equation is needed.  Assuming that dualist solutions do not exist and that continuous generalizations are needed, Continuous Spontaneous Localization (CSL) is argued to be the unique Markovian solution.

Strengths:

Regarding the measurement problem, Gisin states:

Let me stress that I consider the quantum measurement problem as a serious and real physics problem. It is serious because without a solution quantum theory is incomplete, as discussed earlier. It is real in the sense that its solution will provide new physics, with new and testable predictions. Hence it is not merely a matter of interpretation.

Many philosophers that we have read have been attempting to provide or debate interpretations of the two von Neumann postulates of quantum mechanics rather than acknowledging that these postulates are incomplete and require further work in order to determine the conditions under which measurement occurs and the physics of measurement.  Perhaps this is because Bohr at some point believed that little more could be done on this problem. However, modern theoretical and experimental work on entanglement suggests that Bohr was wrong on this point.

Gisin’s viewpoint largely coincides with what we have defined as the physical measurement problem [1 p. 92-98], as opposed to the philosopher’s measurement problem [1, p. 92-98]. Gisin is among the surprisingly few that sufficiently understand the measurement problem to see the need to go further than simply providing an interpretation to resolve the measurement problem. 

Gisin believes that determinism plus entanglement is intractable, and that collapses are needed in a theory. Moreover, that a non-deterministic generalization of quantum mechanics is needed that is both linear in density operator and non-linear in wavefunction. And that CSL is largely a unique theory within the class of continuous Markovian collapse theories that is linear in density operator and non-linear in wavefunction.  Gisin indicates that CSL can be put into a form similar to GRW for which position localization occurs asymptotically in time. Gisin admits however that CSL is not extendable to a satisfactory relativistic theory.  We agree with Gisin on all these points.

Weaknesses:

We agree with Gisin on the basics of the measurement problem, the need for a collapse theory, the need for a theory that is non-linear in wave function and linear in density operator, and the need for a non-deterministic approach, and the division of approaches into dualist and non-dualist.  This is important as a substantial number of people don’t understand the measurement problem sufficiently to see the necessity of these issues. 

On the other hand, beyond these issues we do not agree with Gisin on the details regarding the approach to take to resolve the problem. In regards to CSL, Gisin admits that CSL is not extendable to a satisfactory relativistic theory.  However, Gisin failed to mention that CSL does not conserve energy, neither on average nor on every trial [2]. One can perhaps hypothesize a source of this energy, but such a source is strictly conjecture at this time.

Internon theory (the approach is described at  www.internon.com) is precisely a “dualist” theory that Gisin is against. We are perhaps the only group that has been seriously developing dualistic theory over a span of many years and believe there are shortcomings in Gisin’s exposition. We expect to write a paper on the basics of the approach in internon theory in the future and will more fully delineate where we disagree with Gisin on the approach; for now, one such issue that we elaborate further on below is what it means to be quantum.

Gisin refers throughout to quantum stuff and non-quantum stuff whereby the non-quantum stuff cannot be in a superposition.  In particular he states:

I argue that either there are several kinds of stuffs out there, i.e., physical dualism, some stuff that respects the superposition principle and some that doesn’t, or there are special configurations of atoms and photons for which the superposition principle breaks down. Or, and this I argue is the most promising, the dynamics has to be modified, i.e., in the form of a stochastic Schrödinger equation.

However, historically the discovery of the quantum began largely with Planck’s discovery of the quantum of action in 1900.  The quantum of action initially had its roots in what Bohr, before 1926, describes as the irrational and non-causal aspects of physics. When Schrödinger proposed his deterministic equation in 1926 and predicted the possibility of large-scale superpositions, many began associating quantum mechanics with the existence of superpositions. However, Bohr argued with Schrödinger that his deterministic quasi-classical equation could not be sufficient to describe quantum phenomenon on the basis of the lack of the irrational and non-causal aspects of Planck’s quantum of action needed to describe aspects of thermodynamics.  Bohr was correct and Born’s rule was added to von Neumann’s formalized quantum mechanics, and hence there is currently a dual description of Nature.  Furthermore, this description of the quantum is complementary in Bohr’s theory as both causal and non-causal modes of state time evolution are required for a full description. 

The concept of the “quantum” represents the physical objects and not just their time evolution or whether they are in a superposition. Hence the “quantum” applies equally well to the two complementary manners of time evolution of the quantum states that are implied in the two postulates of quantum mechanics. This was Bohr’s intention and we certainly do not agree with Gisin’s characterization of objects that do not exist in a superposition as being non-quantum. The quantum objects themselves versus the potential time evolutions of their states are two separate issues and Gisin in our view is mixing apples and oranges. That is, even if an object were to not be in a superposition it is nonetheless a quantized object in our internon theory.

Conclusions:

There are largely two major classes of physical theories that explain measurement: 1) dualist and 2) non-dualist. If one can conclude from a trivial argument that dualist theories are incorrect and that a continuous, Markovian transition is required that is not Lorentz invariant nor conserves energy without an additional energy source, then the largely unique theory is within the class of CSL theory.

Regarding Gisin’s statement:

I don’t think that dualism is the right solution for the measurement problem. It might be that in some decades, if the measurement problem remains without significant progress, one may have to revisit a dualistic solution.

To this we ask, do you expect to live over 100? …

Minor Issues:

It is stated, “For chaotic systems, on the contrary, these infinitesimal digits quickly dominate the dynamics. Hence, since these mathematical infinitesimal digits do not physically exist, chaotic dynamical system are not deterministic.”  We expect that the issue of the infinitesimal digits encountered in chaotic systems is irrelevant to the issue of the physics of non-determinism, and that the physics of non-determinism impacts digits that both physically exist and are significant i.e. that are far from being infinitesimal. Hence although chaotic systems maybe an example of the possibility of non-deterministic evolution when certain digits cannot be physically manifest, it is not the only example nor do we expect it to be a particularly relevant example.

[1] M. J. Steiner, R. W. Rendell, The Quantum Measurement Problem, Inspire Institute (2018).

[2] A. Bassi, E. Ippoliti, and B. Vacchini, On the energy increase in space-collapse models, J. Phys. A. Math. Gen., vol. 38, p. 8017, 2005